The life cycle of orogenic belts is governed by the competition between compressional tectonic forces that build topography and gravitational forces that destroy it through extension. In mature orogens, extension is commonly thought to occur through viscous flow within a weak crustal channel (WCC), driven by topographic gradients between mountain belts and their margins. This process is expressed in the upper crust as normal faulting atop high mountain belts, such as the Tibetan Plateau and the Apennines. However, the mechanical link by which flow within the WCC drives extension in the brittle upper crust remains poorly understood. Here, we present a novel physical model, derived from 1st principles, that describes how flow within the WCC leads to orogenic extension by normal faulting and allows for the quantitative prediction of deformation rates. We combine our analytical model with 2D numerical simulations to show that topographic gradients drive flow within the WCC, which in turn generates basal tractions on the overlying brittle crust, thereby promoting extension along normal faults. Our results demonstrate that orogenic extension is only possible when a sufficiently weak WCC is present (η_WCC≤10^21 Pa*s) and the orogen exceeds a critical elevation threshold, h_min,. This threshold is determined by the frictional strength of the upper crust and the basal shear stress exerted by the WCC. We identify a physical relationship linking extension rates to upper-crustal fault strength, orogenic height, and WCC viscosity and thickness. High extension rates occur where faults are weak and topography is high (h>>h_min), particularly when combined with a thick, low-viscosity WCC. Conversely, stronger faults, lower elevations, or thinner and more viscous WCC suppress extension. Applying this framework to the Apennines and the Tibetan Plateau, we demonstrate that the observed scaling between surface extension rates and elevation provides quantitative constraints on WCC rheology and upper-crustal fault strength.